Application of nonlinear deformation algebra to a physical system with P\"oschl-Teller potential

We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31 (1998) 6473), wherein a nonlinear deformation of su(1,1) involving two deforming functions is realized in the exactly solvable quantum-mechanical problem with P\" oschl-Teller potential, and is used to derive the well-known su(1,1) spectrum-generating algebra of this problem. We show that one of the defining relations of the nonlinear algebra, presented by the authors, is only valid in the limiting case of an infinite square well, and we determine the correct relation in the general case. We also use it to establish the correct link with su(1,1), as well as to provide an algebraic derivation of the eigenfunction normalization constant.Comment: 9 pages, LaTeX, no figure

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr\"odinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199

Comparative multi-modal, multi-scale residual stress evaluation in SLM 3D-printed Al-Si-Mg alloy (RS-300) parts

SLM additive manufacturing has demonstrated great potential for aerospace applications when structural elements of individual design and/or complex shape need to be promptly supplied. 3D-printable AlSi10Mg (RS-300) alloy is widely used for the fabrication of different structures in the aerospace industry. The importance of the evaluation of residual stresses that arise as a result of the 3D-printing process’ complex thermal history is widely discussed in literature, but systematic assessment remains lacking for their magnitude, spatial distribution, and comparative analysis of different evaluation techniques. In this study, we report the results of a systematic study of residual stresses in 3D-printed double tower shaped samples using several approaches: the contour method, blind hole drilling laser speckle interferometry, X-ray diffraction, and Xe pFIB-DIC micro-ring-core milling analysis. We show that a high level of tensile and compressive residual stresses is inherited from SLM 3D-printing and retained for longer than 6 months. The stresses vary (from −80 to +180 MPa) over a significant proportion of the material yield stress (from −⅓ to ¾). All residual stress evaluation techniques considered returned comparable values of residual stresses, regardless of dramatically different dimensional scales, which ranged from millimeters for the contour method, laser speckle interferometry, and XRD down to small fractions of a mm (70 μm) for Xe pFIB-DIC ring-core drilling. The use of residual stress evaluation is discussed in the context of optimizing printing strategies to enhance mechanical performance and long-term durability

Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations

A short review of the main properties of coherent and squeezed states is given in introductory form. The efforts are addressed to clarify concepts and notions, including some passages of the history of science, with the aim of facilitating the subject for nonspecialists. In this sense, the present work is intended to be complementary to other papers of the same nature and subject in current circulation.Comment: 50 pages, misprints corrected, some new references included. To appear in "Integrability, Supersymmetry and Coherent States. A Volume in Honor of Professor Veronique Hussin